Method, system and devices for selective modal control for vibrating structures

ABSTRACT

A method, system and devices to selectively control modal vibrations in an elastic panel with a number of force actuators distributed throughout the surface of the elastic panel to excite/depress the response of one or more vibrational resonant modes included in a prescribed subset. The force actuators are disposed such that prescribed modal excitation/depression may be realized when the actuators are driven by a common source signal.

This application is a national stage application of International PatentApplication No. PCT/US2019/054513, filed Oct. 3, 2019, which claimspriority from U.S. Provisional Application Ser. No. 62/745,307, filedOct. 13, 2018. The entirety of the aforementioned application isincorporated herein by reference.

FIELD

This application relates to a control system for structures where one ormore force actuators are employed to excite or depress structuralvibration, and/or radiated sound.

BACKGROUND

Force actuators have been employed for a number of years toexcite/depress the response of one or more vibrational resonant modes instructures. Techniques for modal excitation/depression can take a numberof forms. One such form is active vibration control with feedback, wherethe response of the structure to a disturbance is first estimated usinga number of sensors distributed on the structure. The sensor signals aresent to a controller, which interprets the sensor signals, and then inresponse, sends a separate drive signal(s) to one or more forceactuators distributed on the structure to reduce or excite thecontributions of certain vibrational resonant modes. The controller theninterprets the corresponding structural response via the sensors, andadjusts the drive signal(s) as needed.

Alternatively, if the vibrational resonant modes of the structure andthe disturbance are known, an array of force actuators may be disposedon the structure to give a prescribed response for a particular subsetof modes. For example, when developing a flat-panel loudspeaker usingthe modal crossover technique, as described in U.S. application Ser. No.15/753,679, which is incorporated herein by reference, the actuatorarray is configured to excite bending modes with desirable soundradiation properties, such as the lowest bending mode of asimply-supported rectangular panel, and depress modes with undesirablesound radiation properties.

Regardless of the technique used for selective modal control, the drivesignals applied to the force actuators are dependent on the position ofthe actuators relative to the nodal lines of each vibrational resonantmode. For a given drive signal, an actuator located near a nodal linewill exert relatively little force on a particular mode, while anactuator located on an antinode will exert maximum force on the mode.Since these control techniques are designed to address a number of modessimultaneously, the relative amplitudes of the signals applied to eachactuator must be weighted by their position relative to the nodal linesof each mode using a weighting function to achieve a prescribedvibrational response. For an arbitrary array layout, implementing theweighting function would require a number of additional electronics,which can add to the cost of manufacturing and decrease the reliabilityof the product.

Therefore, there is need for devices, systems and methods that overcomethe challenges of producing sound absent unwanted distortions in amanner that is simpler and more cost-effective.

SUMMARY

An aspect of the application is a device for radiating sound,comprising: a panel, wherein the panel possesses one or more vibrationalresonant modes; a plurality of dynamic force actuators, wherein thedynamic force actuators are positioned in an array at locations on thepanel that are determined to significantly actuate a selected panel modein a given frequency range while minimizing the excitation of all othermodes in the selected frequency range, wherein the selected mode isdriven with significant force when the actuators are applying equalforce to the panel; and a common signal source, wherein the source isconnected to the plurality of dynamic force actuators, and wherein asignal is received by each of the plurality of force actuators from thecommon signal source, and further wherein the dynamic force produced bythe plurality of force actuators upon the panel generates a radiation ofsound from the panel in a selected frequency band. Often, for thepurpose of radiating sound from the panel in a selected panel mode isthe lowest mode of vibration of the panel in which all points of thepanel move in phase with one another, i.e., there are no nodal lines inthe panel surface apart from the boundaries.

Another aspect of the application is a method of controlling radiationof sound, comprising the steps of: selecting a panel, wherein the panelpossesses one or more vibrational resonant modes; positioning aplurality of dynamic force actuators, wherein the dynamic forceactuators are positioned in an array at optimized locations on the panelto significantly actuate a selected panel mode in a given frequencyrange while minimizing the excitation of all other modes in the selectedfrequency range, wherein the selected mode is driven with significantforce when the actuators are applying equal force to the panel; linkinga common signal source to the plurality of dynamic force actuators via amodal crossover network; receiving a signal from the common signalsource, wherein the signal is received by each of the plurality of forceactuators; and applying a dynamic force generated by the plurality offorce actuators upon the panel to output a radiation of sound from thepanel, wherein the sound is in a selected frequency band.

Another aspect of the application is a method of radiating sound by thedevice or system described herein, which may be comprised of any one ofthe various embodiments described herein, comprising the steps of:positioning the device or system described herein inside or outside amobile structure; radiating sound using the device of the presentapplication inside or outside the mobile structure. In certainembodiments, the mobile structure is a transportation vehicle. Incertain embodiments, the mobile structure is a mobile electronic device.In certain embodiments, the mobile structure is an acoustic radiator.

Another aspect of the application is a system for controlling theradiation of sounds, comprising: a device as described herein, which maybe comprised of any one of the various embodiments described herein; aprogrammable computer processor, wherein the computer processor isnetworked to the device described herein, and further wherein thecomputer processor controls the signal produced by the common signalsource of the device.

There are a variety of embodiments which may be embodied separately ortogether in combination in the various aspects of this application; anindependent listing of an embodiment herein below does not negate thecombination of any particular embodiment with the other embodimentslisted herein in practicing the various aspects of the application.

In certain embodiments, the device has a panel that is flat and has ashape selected from the group consisting of circular, rectangular orsquare. In certain embodiments, the device has a common signal sourcewhich is a single amplifier.

In certain embodiments, the actuators are positioned on the structure toaddress a prescribed subset of vibrational resonant modes. In certainembodiments, the actuators are positioned to cancel the excitation ofone or more of the panel's vibrational resonant modes included in theprescribed subset.

In certain embodiments, the actuators are positioned such that they lieon nodal lines, or are so disposed in anti-nodal regions such that thenet force acting on selected panel modes approaches zero. In certainembodiments, the prescribed modal set comprises of all the panel modesthat resonate within a prescribed bandwidth. In certain embodiments, theforce actuators are wired in selected series/parallel configurations toproduce a target total electrical impedance. In certain embodiments, thearray is employed in conjunction with one or more independently drivenindividual force actuators on the panel.

In certain embodiments, the force actuators are electromagnetic coildrivers. In certain embodiments, the force actuators comprisepiezoelectric materials. In certain embodiments, the dynamic forceactuators are positioned in an array at optimized locations on the panelto significantly actuate only the lowest panel mode in a given frequencyrange. In certain embodiments, a modal crossover network connects theplurality of dynamic force actuators, and wherein the common signalsource is connected to the plurality of dynamic force actuators via themodal crossover network.

In certain embodiments, the piezoelectric materials comprise ceramic. Incertain embodiments, the piezoelectric materials comprise organicpolymers. In certain embodiments, the organic polymers comprisepolyvinylidene fluoride (PVDF). In certain embodiments, the signal isselected from the group consisting of digital, analog, partiallydigital, and partially analog signal.

In certain embodiments, the signal is an audio signal. In certainembodiments, the signal comprises information selected from one or moreof speech, music, and other naturally occurring sounds, or artificiallysynthesized sounds.

In certain embodiments, the system further comprises a data receiver,wherein the data receiver is networked to the programmable computerprocessor, and further wherein data that is input into the system viathe data receiver is transformed into the signal output by the commonsignal source of the device. In certain embodiments, the data receiveris a microphone. In certain embodiments, the data receiver is a mobileelectronic device or a vibration sensor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a structure with force actuators arranged to excite/depress aset of vibrational resonant modes when driven by the input signal viathe amplifier;

FIG. 2 shows two panel structures of different aspect ratios arrangedwith an array of twelve force actuators operating in conjunction withindependently driven individual actuators;

FIG. 3 is an example layout with four actuators configured to excite the(1,1) mode of a rectangular panel and depress the excitation of a numberof other modes;

FIG. 4 is an example layout with four actuators configured to excite the(2,1) mode of a rectangular panel and depress the excitation of a numberof other modes;

FIG. 5 is an example layout with eight actuators configured to excitethe (1,1) mode of a rectangular panel and depress the excitation of anumber of other modes;

FIG. 6 is an example layout with eighteen actuators configured to excitethe (1,1) mode of a rectangular panel and depress the excitation of anumber of other modes;

FIG. 7 shows optimized locations for four actuators on a simulatedpanel. Locations are shown relative to normalized dimensions;

FIG. 8 shows optimized locations for eight actuators on the simulatedpanel. Locations are shown relative to normalized dimensions;

FIG. 9 shows optimized locations for eleven actuators on the simulatedpanel. Locations are shown relative to normalized dimensions;

FIG. 10 shows average surface velocities and vibrometer images for theacrylic panel described in the text under excitation from a singleactuator as well as the three optimized arrangements; and

FIG. 11 shows a photo of the experimental panel setup with 11 actuatorsconnected in series.

While the present disclosure will now be described in detail, and it isdone so in connection with the illustrative embodiments, it is notlimited by the particular embodiments illustrated in the figures and theappended claims.

DETAILED DESCRIPTION OF THE INVENTION

Reference will be made in detail to certain aspects and exemplaryembodiments of the application, illustrating examples in theaccompanying structures and figures. The aspects of the application willbe described in conjunction with the exemplary embodiments, includingmethods, materials and examples, such description is non-limiting andthe scope of the application is intended to encompass all equivalents,alternatives, and modifications, either generally known, or incorporatedhere. Unless otherwise defined, all technical and scientific terms usedherein have the same meaning as commonly understood by one of ordinaryskill in the art to which this application belongs. One of skill in theart will recognize many techniques and materials similar or equivalentto those described here, which could be used in the practice of theaspects and embodiments of the present application. The describedaspects and embodiments of the application are not limited to themethods and materials described.

As used in this specification and the appended claims, the singularforms “a,” “an” and “the” include plural referents unless the contentclearly dictates otherwise.

Ranges may be expressed herein as from “about” one particular value,and/or to “about” another particular value. When such a range isexpressed, another embodiment includes from the one particular valueand/or to the other particular value. Similarly, when values areexpressed as approximations, by use of the antecedent “about,” it willbe understood that the particular value forms another embodiment. Itwill be further understood that the endpoints of each of the ranges aresignificant both in relation to the other endpoint, and independently ofthe other endpoint. It is also understood that there are a number ofvalues disclosed herein, and that each value is also herein disclosed as“about” that particular value in addition to the value itself.

This application describes a control system for structures where one ormore force actuators are employed to excite or depress structuralvibration, and/or radiated sound. In particular, the present applicationdiscloses a system and method of placing dynamic force actuators on aflat panel such that when they are all supplying an equal pressure onthe panel preferably only the lowest mode is significantly actuatedwithin a given frequency range.

If the vibrational resonant modes of the structure are known, an arrayof force actuators may be disposed on the structure to give a prescribedresponse for a particular subset of modes. The drive signals applied tothe force actuators are dependent on the position of the actuatorsrelative to the nodal lines of each vibrational resonant mode. For agiven drive signal, an actuator located near a nodal line will exertrelatively little force on a particular mode, while an actuator locatedon an antinode will exert maximum force on the mode.

An optimization method is described herein for determining the placementof actuators such that they significantly excite a selected mode whiledepressing the other modes in a desired subset of structural modes whendriven by a common source. The need for a weighting function, and theadditional costs associated with implementing the weighting function forselective modal excitation are eliminated by optimizing the placement ofthe force actuators.

The System

FIG. 1 shows a particular embodiment of the system described herein. Thestructure (100) is an elastic panel with force actuators (101) arrangedupon it to exert pressure upon the panel to excite/depress a set ofvibrational resonant modes when driven by the input signal (102) via theamplifier (103) networked to the actuators by a wire (104). The systemmay also comprise a computer network, including a computer processor(not shown). One of ordinary skill will understand that pressure asreferred to herein is force per unit area and the force actuators applyequal pressure (e.g., force per unit area) at each of their points ofcontact with the elastic panel. One of ordinary skill will understandthat the force actuators are designed to have full contact with thepanel in an equal and consistent manner, so as to avoid differences inthe contact areas between the actuators and the panel. Ensuring thatthere are no differences in contact area between the actuators and thepanel avoids the application of different forces by different actuatorsto the elastic panel. FIG. 2 shows a pair of working embodiments of thesystem of FIG. 1 .

The panel used in the method, device and systems herein is an elasticpanel. The panel can be made of materials including, but not limited to,partially or fully from aluminum, glass, wood, plastics, both ferrousand non-ferrous metals, combinations thereof, and the like, and othermaterials having elasticity. Certain embodiments described herein belowuse an acrylic panel with 4, 8, and 11 actuators that demonstratesuccessful operation of the actuator arrangements. However, one ofordinary skill will understand that the method, device and systemsdescribed herein are not limited to use of an acrylic panel.

In the method, device or systems described herein, an array of forceactuators excites the flexural vibrations of an elastic panel. Eachindividual force actuator in itself is not a sound amplifying device anddoes not radiate appreciable acoustic energy by itself. However, when aforce actuator is mounted to an elastic panel, as described herein,bending vibrations of the elastic panel are excited, which in turn leadsto the radiation of acoustic energy by the vibrating elastic panel. If asingle force actuator is driven by an audio signal it excites theentirety of the elastic plate and sound will be radiated by the entirepanel. If one were to employ a single force actuator mounted to anelastic panel, the higher order bending modes of the elastic panel wouldbe excited unavoidably.

Force actuators in an array work together to avoid the excitation ofhigher order bending modes of the panel. Preferably, only the lowestorder bending mode of the panel is excited and exciting other bendingmodes is avoided, since this can lead to sonic distortions. The mannerin which the audio signal is divided into frequency bands and the forceactuator signals are controlled to achieve the controlled excitation ofcertain panel modes, while explicitly avoiding the excitation ofunwanted panel modes, is through the “modal crossover” method.

The key function of a “modal crossover network” is to employ an array offorce actuators to control which bending modes of the vibrating panelare excited. In embodiments using a modal crossover network, signals indifferent frequency ranges are sent to the individual force actuatorswith varying gain factors chosen to excite specific modes of vibrationof the elastic panel, the entire surface of which then radiates sound.The signals sent to the array of actuators are scaled appropriately sothat the plurality of actuators will excite a specific vibrational modeof the elastic panel. For example, to excite the lowest vibrational modeof an elastic panel the actuators nearer to the center of the panelshould have higher gain factors, those closer to the boundaries shouldemploy lower gain.

In certain embodiments, the method, system and devices described hereinmay be used without a modal crossover network. Furthermore, although itis preferred that the elastic panel be excited in its lowest bendingmode, while canceling the response of all other modes within the set,the method, system and devices described herein are not limited by thispreference.

In other embodiments, the method, system and devices described hereinmay be used to excite a panel mode, or combination of modes, other thanthe fundamental vibrational resonant mode (e.g., for purposes of noisecanceling). One of ordinary skill will understand how to adapt themethod, system and devices described herein to individually excite anyof the panel modes within the set of panel modes. The method, system anddevices described herein are not limited to excitation of thefundamental vibrational resonant mode, but may be extended for any modewithin the set.

FIGS. 3-6 show example layouts with differing numbers of actuatorsconfigured to excite the particular modes of a rectangular elastic paneland depress the excitation of a number of other modes. In particular, incomparing FIG. 3 and FIG. 4 , one can observe that the shifting inposition of the actuators on the panel relative to the nodal lines ofthe panel results in the excitation/depression of different panel modes.In FIG. 3 , the (1,1) mode is excited by 3.000 Pa, while all other modesare canceled; in FIG. 4 , the (2.1) mode is excited by 3.4641 Pa, whileall other modes are canceled. In FIG. 5 , although eight force actuatorsare used, their positioning is such that only the (1,1) mode is excited,while all others are canceled. In FIG. 6 , which used eighteen forceactuators, it can be observed that the panel is most significantlyexcited in the (1,1) mode, with the other modes being canceled (or verymarginally excited).

One of ordinary skill will understand that the method, system anddevices described herein are not limited by the particular shape or sizeof the panel. The flat elastic panel may be circular, square,rectangular, etc. Preferably, the flat panels have edges that are eithersimply supported or clamped in contrast to distributed-modeloudspeakers, whose edges are generally assumed to be free orelastically supported.

Vibroelastic Behavior of Elastic Panels

Eq. (1) is used to describe the vibroelastic behavior of a forced platewith dimensions L_(x) by L_(y) [Cremer, L., Heckl, M., and Peterson, B.,Structure-Borne Sound, Springer, 3 edition, 2005]. The externallyapplied pressure distribution on the plate is represented by p(x,y,t),and the spatially distributed out-of-plane displacement of the panel isrepresented by u(x,y,t), where (x,y) is the location on the panel and trefers to time. The notation u(x,y,t) represents the second temporalderivative of u(x,y, t). D is a quantity referred to as the ‘bendingstiffness’ of the panel, ρ is the density of the panel material, and his the panel thickness.D∇ ⁴ u(x,y,t)+ρhü(x,y,t)=p(x,y,t)  (1)Modal Decomposition

The Rayleigh-Ritz solution to (1) above considers the plate'sdisplacement profile to be the sum of an infinite number of orthogonalvibrational modes [Fuller, C., Elliott, S., and Nelson, P., ActiveControl of Vibration, Associated Press, 1996] and is given in Eq. (2)below. The actual shapes of the modes and their second order resonantbehavior are subject to the boundary conditions of the panel [Berry, A.,Guyader, J.-L., and Nicolas, J., “A General Formulation for the SoundRadiation from Rectangular, Baffled Plates with Arbitrary BoundaryConditions,” J. Acoust. Soc. Am., 88(6), pp. 2792-2802, 1990; Fletcher,N. H. and Rossing, T. D., The Physics of Musical Instruments, Springer,2 edition, 1998; Li, W. L., “Vibroacoustic analysis of rectangularplates with elastic rotational edge restraints,” Journal Acous. Soc.Am., 120(2), pp. 769-779, 2006]. The mode shape functions will bereferred to as G_(r)(x,y), with r being the mode index. The amplitude ofeach mode is represented by A_(r). Often, two-dimensional structuresmake use of two modal indices, such as m and n; however, it is assumedthat the modes are indexed using r which represents the ordering oftheir resonant frequencies with no loss of generality.

$\begin{matrix}{{u\left( {x,y,t} \right)} = {\sum\limits_{r}^{\;}{A_{r}{G_{r}\left( {x,y} \right)}{e^{j\;\omega\; t}.}}}} & (2)\end{matrix}$

To determine A_(r), the externally applied pressure distributionp(x,y,t) is considered to be comprised of an array of N actuatorelements whose dimensions are small relative to the bending wavelengthon the panel in the frequency range of interest, indexed using theletter n. The small size allows approximation of the pressuredistribution from each driver as δ(x−x_(n))δ(y−y_(n)), where theactuator is positioned at (x_(n),y_(n)). Each actuator element producesa force represented by f_(n), scaled by the factor 4/L_(x)L_(y) toobtain the relevant pressure on the panel [Anderson, D., Heilemann, M.C., and Bocko, M. F., “Flat-Panel Loudspeaker Simulation Model withElectromagnetic Inertial Exciters and Enclosures,” Journal Audio Eng.Soc., 2017]. The actual pressure applied to any given mode, P_(r),depends on the location of the actuator; for example, an actuator placedat the node of a given mode will not be able to excite that mode. In thelow-frequency case of actuators whose dimensions are negligible comparedwith the modal wavelength, the driver-to-mode ‘coupling factors’, whichscale the pressure on the mode supplied by the actuator based onlocation, are given by G_(r)(x_(n),y_(n)).

In the case that N actuators are applying force to the panel, the totalpressure on a given mode, P_(r), is simply the sum of every actuator'spressure on that mode. The respective total pressures on R modes isexpressed in matrix form as

$\begin{matrix}{\begin{bmatrix}P_{1} \\P_{2} \\\vdots \\P_{R}\end{bmatrix} = {{\begin{bmatrix}{G_{1}\left( {x_{1},y_{1}} \right)} & {G_{1}\left( {x_{2},y_{2}} \right)} & \cdots & {G_{1}\left( {x_{N},y_{N}} \right)} \\{G_{2}\left( {x_{1},y_{1}} \right)} & {G_{2}\left( {x_{2},y_{2}} \right)} & \cdots & {G_{2}\left( {x_{N},y_{N}} \right)} \\\vdots & \vdots & \vdots & \vdots \\{G_{R}\left( {x_{1},y_{1}} \right)} & {G_{R}\left( {x_{2},y_{2}} \right)} & \cdots & {G_{R}\left( {x_{N},y_{N}} \right)}\end{bmatrix}\begin{bmatrix}\frac{4f_{1}}{L_{x}L_{y}} \\\frac{4f_{2}}{L_{x}L_{y}} \\\vdots \\\frac{4f_{N}}{L_{x}L_{y}}\end{bmatrix}}.}} & (3)\end{matrix}$

In certain embodiments, the actuator locations are determined byminimizing the ratio of high-order mode pressures to the lowest modepressure when all actuators supply equal pressure.

Optimization Method

An optimization method is described herein for determining the placementof force actuators on the surface of an elastic panel such that they areall driven by a single amplifier yet only excite a single structuralmode in the elastic panel. “Optimized” herein means that a search isperformed to find the actuator locations that maximize the ratio of theforce on the mode that is selected to be excited vs. the sum total ofthe forces on the modes that are non-selected. Preferably, forloudspeakers, the lowest mode is excited.

It is preferable that for a set of N actuators, the N lowest modesshould all have a force of 0 (or nearly 0) aside from the mode that thearray is intended to excite. Preferably, the force on the selected modeto be excited is at least ten times greater than the force on any of theother N modes. For example, in Table 1 below, the lowest mode has aninfinitely higher force than the others in the set. Driverconfigurations (and hence the relative forces exerted on each mode) willchange depending on the number of actuators used. In Table 1 below, theforce on the lowest mode increases as the number of actuators increases.Note that a user can only specify the force on one mode per actuatorused.

Referring to the four actuator case in Table 1 below, the first fourmodes all have a force of 0 other than the lowest mode. In the eightactuator case, the first eight modes all have a force of 0 other thanthe lowest mode. The same is true for the eleven actuator case. It mayalso be observed that some modes other than the first 4/8/11 also have aforce of 0. This depends on the number of drivers used and the aspectratio of the panel. The symmetry of the optimized actuator layout mayallow modes outside of the set to also be depressed. For example, inFIG. 3 , the 5th mode (2,2) experiences a force of 0 (even though thereare only four actuators) due to the symmetry of the optimized layoutrelative to the nodal lines of that particular mode.

However, the optimization method described herein can generally work forany mode, not just the lowest. There are two changes that must be madeto the algorithm to extent its scope of use to any selected mode. Thefirst is that P1 would equal 0 in the column matrix in eq (4), and theforce/pressure would be nonzero in a different row depending on whichmode is selected. The second change is that the column matrix of 1's onthe right side of eq (4) may have to have one or more −1's to compensatefor the phase changes needed to excite other modes. The phase changescan be implemented by switching the polarity (which ends are connectedto +− signal) of the actuators, so they still may be excited by a commonsource. An embodiment is shown in FIG. 4 , where the second lowest modeis the one excited, and the lowest mode, among others, is minimized.“Minimize” herein does not imply a certain threshold level, but ratherto minimize the excitation of unwanted (non-selected) modes. One ofordinary skill will understand that the choice of selected mode or meansof implementing appropriate phase changes is not limiting on theinvention herein.

The preferred goal of the method and systems described herein is toexcite only the lowest panel mode using an array of actuators supplyingthe same forces. This means configuring Eq. (3) above such that

$\begin{matrix}{\begin{bmatrix}P_{1} \\0 \\\vdots \\0\end{bmatrix} = {{\begin{bmatrix}{G_{1}\left( {x_{1},y_{1}} \right)} & {G_{1}\left( {x_{2},y_{2}} \right)} & \cdots & {G_{1}\left( {x_{N},y_{N}} \right)} \\{G_{2}\left( {x_{1},y_{1}} \right)} & {G_{2}\left( {x_{2},y_{2}} \right)} & \cdots & {G_{2}\left( {x_{N},y_{N}} \right)} \\\vdots & \vdots & \vdots & \vdots \\{G_{R}\left( {x_{1},y_{1}} \right)} & {G_{R}\left( {x_{2},y_{2}} \right)} & \cdots & {G_{R}\left( {x_{N},y_{N}} \right)}\end{bmatrix}\begin{bmatrix}1 \\1 \\\vdots \\1\end{bmatrix}}.}} & (4)\end{matrix}$

The goal of the optimization is to determine actuator locations (x₁,y₁)through (x_(N),y_(N)) such that the pressure P₁ is maximized andpressures P₂ through P_(R) are minimized. The optimization thereforeformulated as

$\begin{matrix}{{\underset{\sum_{i}{({x_{i},y_{i}})}}{argmin}\frac{\sqrt{1 + {\sum\limits_{r = 2}^{R}P_{r}}}}{P_{1}}}{where}} & (5) \\{0 < x_{i} < {L_{x}\mspace{14mu}{and}\mspace{14mu} 0} < y_{i} < {L_{y}.}} & (6)\end{matrix}$

There is no explicit limit on R, the number of modes which can be scaledto an excitation pressure of zero using N actuators. Certain embodimentsdiscussed herein use R=2N, or twice as many modes as actuators,analogous to the Nyquist rate of time-sampled data.

Computer Systems

In certain embodiments the device or system herein may be controlled andnetworked via a computer system, the computer system includes a memory,a processor, and, optionally, a secondary storage device. In someembodiments, the computer system includes a plurality of processors andis configured as a plurality of, e.g., bladed servers, or other knownserver configurations. In particular embodiments, the computer systemalso includes an input device, a display device, and an output device.In some embodiments, the memory includes RAM or similar types of memory.In particular embodiments, the memory stores one or more applicationsfor execution by the processor. In some embodiments, the secondarystorage device includes a hard disk drive, floppy disk drive, CD-ROM orDVD drive, or other types of non-volatile data storage. In particularembodiments, the processor executes the application(s) that are storedin the memory or the secondary storage, or received from the internet orother network. In some embodiments, processing by the processor may beimplemented in software, such as software modules, for execution bycomputers or other machines. These applications preferably includeinstructions executable to perform the functions and methods describedherein. The applications preferably provide GUIs through which users mayview and interact with the application(s). In other embodiments, thesystem comprises remote access to control and/or view the system.

METHODS OF USE

In certain embodiments the device and systems described herein may beused in connection to sound transmission from devices including, but notlimited to, mobile phones, electronic notepads, electronic tablets,electronic automobile dashboards (e.g., in ambulances or cars used formedical-related purposes), electronic motorcycle dashboards, electronicwristbands, electronic neckwear, wall-mounted screens, portable monitors(e.g. wheeled monitors in medical facilities), electronic headbands,electronic helmets, electronic eyewear (e.g. glasses with lens that candisplay information in real time to the wearer), electronic rings,networked computers (e.g. personal computers), remote viewing technology(e.g. rural doctor client-patient communication devices) and portableelectronic devices in general. In certain embodiments, the device may bea vibrational sensor, such as a piezoelectric or PVDF sensor, oraccelerometer.

The present application is further illustrated by the following examplesthat should not be construed as limiting. The contents of allreferences, including patent applications, such as U.S. application Ser.Nos. 15/255,366; 15/778,797; and U.S. Prov. App. Nos. 62/745,324;62/745,314, cited throughout this application, as well as the Figuresand Tables, are incorporated herein by reference.

Examples

Results are presented herein for actuator placement on a simulatedacrylic plate which has dimensions L_(x)=38 cm, L_(y)=28 cm, and h=6 mm.The resonant frequency of each mode must be calculated so that the modeindices are properly ordered when performing the optimization routine.Assuming clamped edges, the resonant frequency of a mode with index r(corresponding to two directional indices m_(r) and n_(r)) is calculatedusing an empirical formula given below [Mitchell, A. K. and Hazell, C.R., “A Simple Frequency Formula for Clamped Rectangular Plates,” J.Sound Vib., 118(2), pp. 271-281, 1987]:

$\begin{matrix}{{\omega_{0_{r}} = {\sqrt{\frac{D}{ph}}{\Psi^{\prime}}_{r}}}{where}} & (7) \\{{\Psi^{\prime}}_{r} = {\left( \frac{\left( {m_{r} + {\Delta\; m_{r}}} \right)\pi}{L_{x}} \right)^{2} + {\left( \frac{\left( {n_{r} + {\Delta\; n_{r}}} \right)\pi}{L_{y}} \right)^{2}{and}}}} & (8) \\{{\Delta\; m_{r}} = {{\frac{1}{\left( \frac{n_{r}L_{x}}{m_{y}L_{y}} \right)^{2} + 2}\Delta\; n_{r}} = {\frac{1}{\left( \frac{m_{r}L_{y}}{n_{r}L_{x}} \right)^{2} + 2}.}}} & (9)\end{matrix}$

For acrylic, the following material values are used: D=8:2 Pa m andρ=1180 kg/m³. Mode shapes take the form

$\begin{matrix}{{G_{r}\left( {x,y} \right)} = {{\sin\left( \frac{m_{r}\pi\; x}{L_{x}} \right)}\mspace{14mu}{{\sin\left( \frac{n_{r}\pi\; y}{L_{y}} \right)}.}}} & (10)\end{matrix}$

The optimization routine is performed using the MATLAB optimizationtoolbox (see, e.g., www.mathworks.com/products/optimization.html).Actuator location results are shown for several values of N actuators inthe array in FIGS. 7, 8, and 9 , which show certain embodiments whichtypically represent global optima after accounting for the fact that theordering of the actuators is not important.

Table 1 below lists the pressure on each plate mode when every actuatoris supplying 1 Pa of pressure to the panel after scaling, assuming thethree driving layouts from FIGS. 7, 8, and 9 . Modes in the table arelisted with respect to increasing resonant frequency. Each drivinglayout is able to excite the (1;1) mode with a significant amount ofpressure, and most other modes are driven with very little or nopressure at all. For 4 actuators, the lowest-frequency mode that isdriven with a significant amount of pressure is the (5;1) mode. For 8actuators, the lowest significant mode above the primary is the (1;5)mode. With 11 actuators, the (7;1) mode is the lowest mode significantlydriven.

TABLE 1 Pressure on Mode (Pa) Mode 4 exciters 8 exciters 11 exciters(1, 1) 3.0000 5.7063 7.4813 (2, 1) 0.0000 0.0000 0.0000 (1, 2) 0.00000.0000 0.0000 (3, 1) 0.0000 0.0000 0.0000 (2, 2) 0.0000 0.0000 0.0000(3, 2) 0.0000 0.0000 0.0000 (4, 1) 0.0000 0.0000 0.0000 (1, 3) 0.00000.0000 0.0000 (2, 3) 0.0000 0.0000 0.0000 (4, 3) 0.0196 0.0000 0.0000(3, 3) −0.0001 0.0000 0.0000 (5, 1) −2.9999 0.0000 0.0000 (1, 4) 0.00000.0000 0.0000 (5, 2) 0.0000 0.0000 0.0000 (4, 3) 0.0000 0.0000 0.0000(2, 4) −0.0196 0.0000 0.0000 (6, 1) 0.0000 0.0000 0.0000 (3, 4) 0.00000.0000 0.0000 (5, 3) 0.0001 0.0000 0.0000 (6, 2) −0.0391 0.0010 0.0000(4, 4) 0.0000 −0.0014 0.0000 (1, 5) −2.9999 −5.7063 0.0000 (7, 1) 2.9997−3.5267 −6.3498

Embodiments of the three optimal actuator arrays from FIGS. 7, 8, and 9are arranged on a panel with the same parameters as were simulated inthe discussion above. The commercially available actuators add weightand resonance to the panel [Anderson, D., Heilemann, M. C., and Bocko,M. F., “Flat-Panel Loudspeaker Simulation Model with ElectromagneticInertial Exciters and Enclosures,” Journal Audio Eng. Soc., 2017], aswell as having an annular connection to the panel with outer radius 11mm and inner radius 8:25 mm. These characteristics will add resonancesto the panel and slightly shift the existing resonances, as well asexert a small amount of pressure on modes that are meant to be canceledout.

The panel is epoxied at its edges to a heavy wooden frame, simulatingclamped boundary conditions. While a 6 mm acrylic panel is likely tooheavy to make an effective speaker, the isotropic, homogeneous behaviorof acrylic, its inherently high damping, and the relatively large weightwhen compared with the actuators make it ideal for experimentalvalidation. As noted above, the use of acrylic is in no way limiting onthe methods, systems or devices disclosed herein.

Different numbers of actuators in arrays produce patterns with varyingimpedance; often, it is impossible to chain the actuators in aseries-parallel combination to give the same impedance as another array.For the arrangement with 4 actuators, two series chains of 4Ω actuatorsare wired in parallel to give a 4Ω load. For the 8 actuatorsarrangement, two series chains of 4Ω actuators are placed in parallel togive an 8Ω impedance. For the 11 actuators arrangement, all actuatorsare wired in series to give a 44Ω impedance. A photo of the experimentalsetup with 11 actuators is shown in FIG. 10 . This experiment isperformed using a scanning laser vibrometer at a distance of 1 m at aspatial resolution of 6:8 mm.

Shown in FIG. 11 is the average surface velocity of the panel when usingeach of the three optimized actuator layouts, as well as a singleactuator placed at normalized location (0:37; 0:71) for comparison. FIG.11 demonstrates that the actuator arrangements are successfully able toselectively excite only the lowest panel mode over a wide frequencyband. There is a slight excitation of the (3;1) mode for eacharrangement, near 500 Hz, likely due to the annular shape of theactuators. The lowest mode's resonant frequency is inconsistent betweenthe actuator arrangements due to resonance coupling predicted in[Anderson, D., Heilemann, M. C., and Bocko, M. F., “Flat-PanelLoudspeaker Simulation Model with Electromagnetic Inertial Exciters andEnclosures,” Journal Audio Eng. Soc., 2017]. It is demonstrated that theactuator arrays are successful at exciting only the lowest panel modefor a wide frequency band using commercially available actuators. Theseresults are practically useful for implementation in flat-panelloudspeakers using a modal crossover network.

While various embodiments have been described above, it should beunderstood that such disclosures have been presented by way of exampleonly and are not limiting. Thus, the breadth and scope of the subjectcompositions and methods should not be limited by any of theabove-described exemplary embodiments, but should be defined only inaccordance with the following claims and their equivalents.

The above description is for the purpose of teaching the person ofordinary skill in the art how to practice the present invention, and itis not intended to detail all those obvious modifications and variationsof it which will become apparent to the skilled worker upon reading thedescription. It is intended, however, that all such obviousmodifications and variations be included within the scope of the presentinvention, which is defined by the following claims. The claims areintended to cover the components and steps in any sequence which iseffective to meet the objectives there intended, unless the contextspecifically indicates the contrary.

What is claimed is:
 1. A method of controlling radiation of sound,comprising the steps of: selecting a panel, wherein the panel possessesone or more vibrational resonant modes, wherein the panel is flat;positioning a plurality of dynamic force actuators, wherein theplurality of dynamic force actuators are positioned in an array atoptimized locations on the panel to actuate a selected mode of vibrationof the panel without requiring a weighting function to excite theselected mode of vibration, wherein the selected mode is excited whenthe actuators are applying force to the panel and non-selected modes areminimized when the plurality of dynamic force actuators are applyingforce to the panel; linking a common signal source to the plurality ofdynamic force actuators via a modal crossover network; receiving asignal from the common signal source, wherein the signal is received byeach of the plurality of dynamic force actuators; and applying a dynamicforce generated by the plurality of dynamic force actuators upon thepanel to output a radiation of sound from the panel, wherein the soundis in a selected frequency band.
 2. The method of claim 1, wherein thecommon signal source is a single amplifier.
 3. The method of claim 1,wherein the plurality of dynamic force actuators are positioned on thepanel to address a prescribed subset of the panel's vibrational resonantmodes.
 4. The method of claim 3, wherein the plurality of dynamic forceactuators are positioned to cancel the excitation of one or morevibrational panel resonant modes included in the prescribed subset. 5.The method of claim 3, wherein the prescribed subset comprises all modesthat resonate within a prescribed bandwidth.
 6. The method of claim 1,wherein the plurality of dynamic force actuators are positioned suchthat said plurality of dynamic force actuators lie on nodal lines, orare so disposed in anti-nodal regions such that a net force acting onselected modes approaches zero.
 7. The method of claim 1, wherein theplurality of dynamic force actuators are wired in selectedseries/parallel configurations to produce a target total electricalimpedance.
 8. The method of claim 1, wherein the array is employed inconjunction with one or more independently driven individual forceactuators on the panel.
 9. The method of claim 1, wherein the pluralityof dynamic force actuators are electromagnetic coil drivers.
 10. Themethod of claim 1, wherein the plurality of dynamic force actuatorscomprise piezoelectric materials.
 11. The method of claim 10, whereinthe piezoelectric materials comprise ceramic.
 12. The method of claim10, wherein the piezoelectric materials comprise organic polymers. 13.The method of claim 12, wherein the organic polymers comprisepolyvinylidene fluoride (PVDF).
 14. The method of claim 1, wherein thesignal is selected from the group consisting of digital, analog,partially digital, and partially analog signal.
 15. The method of claim1, wherein the signal is an audio signal.
 16. The method of claim 1,wherein the signal comprises information selected from one or more ofspeech, music, and other naturally occurring sounds, or artificiallysynthesized sounds.
 17. The method of claim 1, wherein the plurality ofdynamic force actuators are positioned in the array at the optimizedlocations on the panel to significantly actuate only the lowest panelmode in a given frequency range.
 18. The method of claim 1, furthercomprising the step of connecting the modal crossover network to theplurality of dynamic force actuators, wherein the common signal sourceis connected to the plurality of dynamic force actuators via the modalcrossover network.
 19. The method of claim 1, wherein the selected modeis the lowest-frequency panel mode.